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I suggest that we do not use the oxymoron "speculative math". It is an obsolete term for pure math. The way I learned math from mathematicians, math is essentially built on logic, is not a science as often falsely stated and does not make any claim on reality although whole branches of math are inspired by the success of modelling reality with the assistance of math. What you probably mean is "speculative physics", e.g. creating physical theories for which we have not yet any empirical base.

Yes, geometry is a part of math. The continuous extrapolation to infinitely small dimensions of geometric forms does not imply anything for reality.